What makes a good researcher?
Abhishek Arora
Anshul Mittal
Raghav Pasari
Stanford University
Stanford University
Stanford University
[email protected]
[email protected]
[email protected]
ABSTRACT
In this paper we investigate the characteristics of a good
researcher and contrast them with that of other researchers
which would give further insights into how to become a good
researcher. For this we analyze the collaboration and citation pattern of an author. Furthermore, we propose a new
metric which takes into account just the local characteristics
of an author and show how well it performs with respect to a
global metric like pageRank in determining the goodness of
an author. For our experiments, we use the DBLP citation
data which has more than four hundred and fifty thousand
papers and close to a million authors.
1. INTRODUCTION
Scientific collaboration and citation practices have been an
important focus for social scientists, seeking to provide insight into scienctific research as an inherently team-based
endeavour. Several studies [4] [8] have also shown the significant effect that such practices are known to have on scientific productivity.
Scientists have traditionally used author collaboration and
paper citation networks to study such practices. These networks are very common in the research community and share
common properties with other well known networks. More
specifically, they are both scale free networks following a
power law degree distribution, having one big central community etc. among other things. While collaboration networks are relevant for understanding the network structure
of scientific fields (Jones et al., 2008), citation networks are
central in providing insight into the hierarchies within a field
and among fields.
However, besides finding general trends in the practices of
the research community as a whole, it will also be interesting
to observe how such practices vary from one researcher to
another and how they are related to one’s scientific merit.
Every advisor has some tips for his/her students with regard to the research practices he/she ought to follow, for
example, always do thorough literature search and cite many
papers, focus on quality rather than quantity etc., however,
little work has been done to evaluate the correlation between
such practices and the scientific merit or influence. In this
paper, we attempt to analyse and throw light on this side
of the story. We consider several such widely accepted standards regarding the collaboration and citation practices, and
evaluate them by developing some novel metrics. In order to
correlate the metric values with an author’s scientific influence, we experiment with several different influence metrics
and pick the best one for our analysis. For the purpose of
our study, we also develop a new kind of network which we
call the ”author citation network”. We explore the general
properties and community structure of this novel network
and compare it with the more standard author collaboration and paper citation networks.
Our study reveals some interesting trends. For example, we
observe that ”good” authors tend to collaborate more with
other ”good” authors emphasizing the importance of peer
group in research. Similarly, our studies reveal that although
the successful authors tend to focus more on the quality of
research, they never seem to compromise on quantity either!
Here, we must note that we don’t have information about the
1st and 2nd authorship, etc. The following sections reveal
these and many more captivating patterns in the citation
and collaboration practices.
The rest of the paper is organized as follows. The next section presents a critical comparison of the previous work in
this domain. In Section 3, we briefly discuss the dataset
that we have used and the different graphs that we have
constructed for analysis. Section 4 discusses the different
metrics used for ranking the authors. We validate these metrics against some well known facts about these researchers
and then use the best metric for analysis in the rest of the
paper. Section 5 explores the citation practices, patterns of
the researchers and their papers, diversity of the communities they publish papers in, how many and what kind of
papers they cite. Section 6 performs similar analysis for an
author’s collaboration practices. In Section 7, we attempt
to learn some important lessons from the career graphs of
such researchers, that is, how the quality and quantity of
their papers tends to change over time and whether there is
any difference in the temporal patterns between them and
others.
2. RELATED WORK
Citation networks have been studied quantitatively almost
from the moment citation databases first became available,
perhaps most famously by Derek de Solla Price [3]. Since
then, several researchers have studied the topological properties and graph statistics of paper citation networks and
proposed generalised models for their formation [1] [12]. Most
recently, Leicht et al. [5] has explored important temporal
characteristics of such networks. However, all these papers
deal with citation networks where the nodes are scientific papers/documents and not the authors themselves. Therefore,
even though they reveal interesting trends about scientific
research, little information can be obtained directly about
the authors themselves.
Similarly, collaboration networks have been the subject of
extensive study to find patterns in the collaboration practices of researchers in various fields. The most notable work
in this domain is by M.E.J. Newman in 2001 [9] [10] where he
answers some pertinent questions concerning such networks
such as the number of collaborators per scientist, size and
properties of giant component, typical distances and centrality measures. In much the same way as citation networks,
other researchers like Bettencourt et al. [7] have also studied
the temporal evolution and properties of such networks.
Most recently, Ding [4] and Wallace et al. [8] have studied
the influence of collaboration networks on citation practices.
More specifically, they try to reveal trends in citations using degrees of separation in collaboration network (including
self-citations). However, all of the above mentioned papers
present an average analysis for all authors and do not present
an analysis of such properties with respect to the influence
of the authors in the scientific community. Moreover, none
of the papers explore the temporal variation in such characteristics.
3. INPUT GRAPHS AND THEIR PROPERTIES
The data set used in the paper is the DBLP papers and citation relation data set available at [6]. It consists of all
database related papers in the DBLP network up to October 2010 (even though the dataset has been previously
advertised as consisting of all computer science researchers,
our results have shown that the dataset is heavily biased
towards the field of databases). The data includes the following attributes for each paper • Unique index id of the paper
• Title of the paper
• List of authors (comma separated)
Using this data set, we contruct three different kinds of
graphs1. Author Collaboration
2. Paper Citation
3. Author Citation
The first two are the more traditional author collaboration and paper citation graphs. In the author collaboration graph, every author is a node and an edge between two
authors indicates that the two collaborated on some paper
at some point in time (please note that such a formulation
will result in multiple small cliques in our graph because
all authors of a particular paper will have all possible edges
amongst themselves). In the paper citation graph, every paper represents a node and an edge from node a to node b
paper a cites paper b. While such a network gives valuable
information about the citations of the papers, we cannot
extract information about the citation practices of authors
directly from this network (there can be multiple heuristics
for deriving this information indirectly, for e.g. summing
over all papers of one author etc.). For this reason, we construct a third network in which every author is a node and
an edge(directed) denotes that one author was cited by the
other in his/her paper. Such a network, hereafter referred
to as the author citation network, can be directly used to
investigate important characteristics of citation practices of
authors. It is important to note here that the author and
paper citation networks are directed whereas the author collaboration network is undirected. Moreover, the author citation and collaboration networks are multi-graphs (multiple
edges can exist between two nodes) whereas the paper citation graph is a simple DAG (directed acyclic graph).
Table 1 lists some properties of the three graphs (the graphs
are shown in Figure 1). In these graphs, the clustering coefficient and SCCs are generated after removing the multiedges. It can be seen that the author collaboration graph
has a high clustering coefficient, small number of SCCs and
large number of nodes in the biggest SCC, all due to the
presence of multiple small cliques in the network. From the
table, it is also evident that the author citation graph is an
aggregator of paper citation graph for every author. It has
higher clustering coefficient and higher number of nodes in
largest SCC and also has lesser number of nodes as compared to paper citation graph (because one author can have
multiple papers). However, it has much more edges than the
paper citation graph due to the presence of multi edges. The
author collaboration graph has much more nodes than the
other two networks because the data set has many papers
about which no citation information is given.
• Year of publication
• Venue of publication
• List of paper ids cited by this paper
In this paper, we restrict our analysis to the paper id, list of
authors, year of publication and other papers cited by the
paper but do not use the title and the venue of publication.
It can also be seen that in each of the plots, the curve first
increases for small values and then declines. This is because
almost every publication tends to have a few collaborators
and some other papers that it cites. Moreover, most papers
also tend to be cited by at least a few papers, leading to the
decline in indegree of citation networks.
Let us now discuss the community structure of these graphs.
(a) Degree distribution of undirected network(s)
(b) In-degree distribution of directed network(s)
(c) Out-degree distribution of directed network(s)
(d) SCC distribution of all networks
Figure 1: Properties of graphs
Table 1: Properties of graphs
Property
Paper Citation Author Citation
Number of Nodes
475886
334764
Number of Edges
2327450
10746625
Average Clustering Coefficient
0.11439
0.35763
Number of SCCs
419193
159840
Percentage of Nodes in Largest SCC
.1081
.5171
3.1 Community structure of the input graphs
In order to determine the community structure of the networks involved, we use the fast agglomerative clustering
method for large networks described in [11]. The method
starts with considering every node to be in a different community. It then performs two phases repeatedly. In the first
phase, we consider the neighbours j of i and we evaluate the
gain of modularity that would take place by removing i from
its community and by placing it in the community of j. The
Author Collaboration
975001
5644866
0.630
46021
.8576
node i is then placed in the community for which this gain
is maximum, but only if this gain is positive. If no positive
gain is possible, i stays in its original community. In the next
phase, the graph is collapsed so that each community acts
as a node in the new graph. While performing the experiments, we ignore all communities with membership below a
certain threshold.
Using this method, we obtain the community structure of
Figure 2: Correspondence between community
structure of paper and author citation networks
the three graphs involved. It is important to note that the
communities in the citation networks will correspond to the
researchers publishing on a particular topic or sub branch
of computer science whereas the communities in the collaboration network may correspond to all researchers working
in a particular institution or a research lab. Figure 2 shows
the correspondence between the communitites of the author
and paper citation networks which are plotted on the X and
Y axis, respectively. The metric,m1 used here ism1 (x, y) =
P
Figure 3: Correspondence between community
structure of author collaboration and author citation networks
a column can have multiple bright values. This is expected
because one research area in databases will have researchers
from many institutions publishing in that area whereas the
database group in one institution is expected to have focus
in a few research areas only.
Having discussed the different charateristics of our networks,
we next move to the measures for finding the influential
authors using these networks.
∀authors∈x fraction of papers of the author in y
#of authors in x
While evaluating this metric, we consider only the top 80%
authors (based on the fraction of their papers lying in the
paper community y) in the author community to remove any
outliers. As is evident from the graph, there is an almost
one to one correspondence between the community structure
of the two networks confirming our hypothesis that both
networks reveal content based communities. The one to one
correspondence is visible as the bright diagonal which says
that the communities have a high score. The majority blue
area shows that most communities do not correspond to each
other.
Figure 3 shows the correspondence between the communitites of the author citation and author collaboration networks which are plotted on the X and Y axis, respectively
(while constructing this plot we consider only those authors
which occur in both networks). The metric plotted here is
the number of authors in the intersection of the two communities divided by the number of authors in the collaboration
network (which is always the smaller of the two communitites). A careful look at the plot reveals that one community in the citation network matches with several communities in the collaboration graph whereas one community in
the collaboration graph has a significant overlap with only
a few citation communities. This corresponds to a row in
the color map having very few (usually 1) bright value but
4.
INFLUENCE METRICS
Ranking of the scientific influence or productivity of authors has been a long standing area of research. Several
researchers have proposed metrics to evaluate a researcher’s
measure of influence in the scientific community. Some of
these are number of papers, number of citations, average
number of citations, H-index, G-index etc. Out of these, Hindex is widely considered to be the best and most standard
metric. These are examples of local metrics which can be
evaluated with only the local information about every node.
However, in our case where we are additionally given the
graph of researchers, a better ranking may be obtained by
obtaining an influence ranking of the nodes in the network.
The next questions, therefore, are that which metric should
be used for such an evaluation and which networks to evaluate it on. First, let us consider the question of which metric
to use. There are several measures which can be used for
such an evaluation, namely, betweenness centrality, closeness centrality, degree centrality, HITS (hubs and authorities), pageRank etc. In this paper, we use the pageRank [2]
to find influential nodes in the network. The pageRank algorithm is an influence metric where a node is considered
important if it is pointed to by other important nodes. If
r is the rank vector of the network and M is the stochastic
adjacency matrix (as defined in [2]), the rank rj for node j
is given by the equations-
H-index
pRankAuCollab
pRankAuCit
numPapers
numCitations
avgCitations
Rank
1
2
3
4
5
Table 2: Pearson correlation of different influence metrics
H-index pRankAuCollab pRankAuCit numPapers numCitations
1.0
0.49
0.65
0.64
0.72
0.49
1.0
0.35
0.70
0.39
0.65
0.35
1.0
0.39
0.90
0.64
0.70
0.39
1.0
0.50
0.72
0.39
0.90
0.50
1.0
0.28
0.05
0.28
0.06
0.29
Table 3: Top 5 authors using different metrics
pageRank in author collaboration pageRank in author citation
Alberto L. Sangiovanni-Vincentelli
Jeffrey D. Ullman
Hans-Peter Seidel
Jim Gray
Thomas s. Huang
E. F. Codd
Donald F. Towsley
C. A. R. Hoare
Ron Kikinis
Donald D. Chamberlin
P
rj = i−>j ri /dout (i)
r = Mr
Coincidentally, the pageRank algorithm derives its inspiration from the citation practices in scientific communities
making it the most relevant evaluation metric for our analysis. It is also among the fastest in the many metrics discussed above (much faster than betweenness) and therefore,
more suitable for the present scenario where we have more
than a million nodes in the graph. We evaluate this metric
on two networks - author collaboration and author citation
network (we don’t use the paper citation network because,
as noted in the previous section, the author citation network
is an aggregator of paper citation network and is much more
suitable for evaluating properties of authors).
Table 2 shows the pearson correlation between the rankings obtained by using different metrics- pRankAuCollab
measures the pageRank in author collaboration network,
pRankAuCit measures the pageRank in author citation network, numPapers ranks on the basis of number of papers,
numCitations uses the total number of citations obtained
by the author and avgCitations uses the number of citations
obtained per paper. It is clearly evident that the pageRank in author citation network is biased towards the number of citations and average number of citations whereas
the pageRank in collaboration network performs poorly visa-vis these metrics and tends to give more weight to the
number of papers (traditionally not considered to be a good
metric of scientific productivity although one that has sadly
become quite omnipresent these days!). An interesting observation is that H-index has higher correlation with the
number of papers than the citation pageRank because the
H-index is necessarily bound by the number of papers of
an author. H-index also has a lower correlation with the
number of citations than the citation pageRank (both have
same correlation with respect to average citations). Finally,
H-index is better correlated with citation pageRank than
the collaboration pageRank.
Table 3 lists the top 5 authors obtained using three metrics
- pageRank in author collaboration network, pageRank in
author citation network and the widely used H-index. By
avgCitations
0.28
0.05
0.28
0.06
0.29
1.0
H-index
Hector Garcia Molina
Jeffrey D. Ullman
David J. Dewitt
Rakesh Agrawal
Scott Shenker
looking at the profiles of these researchers manually and taking into consideration the honours and recognition bestowed
upon these researchers, it can be seen that using pageRank
in the author citation network gives the best indication of
an author’s prominence in the scientific community (3 turing awardees in the top 5). We therefore, use this metric as
a measure of influence in the rest of the paper.
In the next section, we investigate some patterns in the citation practices of the authors with respect to their measured
influence.
5.
CITATION PRACTICES
We want to study the citation practices of author’s in the
author citation network. Here we hypothesize that highly
ranked authors tend to cite one another more, whereas low
ranked authors do not cite each other much - they also primarily cite highly ranked authors. This is fairly obvious as
highly ranked authors are highly ranked because they receive many citations. For this we construct a sub-graph of
the author citation graph by considering only the nodes with
ranks within a certain fixed range of a given node’s rank so
that only those nodes which have pageRank very close to the
given node’s remain in the network. We then find the clustering coefficient of the resulting sub-graph. In Figure 4, we
plot a graph of this clustering coefficient of sub-graph for different rank nodes. For all the plots where we have page rank
on the x-axis (in all further sections too), we sort the nodes
by their pageRank in descending order, take points spaced
by some fixed value(50), centre a bin around the points with
bin size(60) and averaged the y-values in that bin.
From this graph we can see that highly ranked authors tend
to cite one another a lot (high clustering coefficient) whereas
the low ranked authors don’t cite each other much. This is
in line with our hypothesis.
5.1
Trends on Papers the author writes
Here, we would like to answer how uniformly are the papers
of an author are cited. We have used Jain’s fairness index
as a measure of uniformity. Given n buckets and xi as the
number of balls in bucket i, the uniformity in the ball distribution across the buckets can be measured using Jain’s
is more likely to have low uniformity in their citation as only
a few papers would be quality papers. Also, we don’t have
information about the 1st author, 2nd author, etc about a
paper in our dataset. A reputed author is likely to have
many papers as last author(mostly with his PhD students
and other collaborators in the community). Figure 6 verifies
the fact highly ranked authors indeed have relatively large
number of papers.
Figure 4: Average clustering coefficient in citation
network with similar rank authors
fairness index as:
J(x1 , x2 , . . . , xn ) =
P
2
( n
i=1 xi )
P
2
n. n
i=1 xi
In our context, buckets are the papers of an author and balls
are the number of citations of the paper. Figure 5 shows the
plot of the uniformity in paper citation versus page rank of
the author in the author citation network. We observe that
the paper citation uniformity shows an increasing trend with
rank.
Figure 6: Number of papers with decreasing author
ranks
Above, we could have also used entropy for measuring uniformity instead of Jain’s fairness index. It is just that we
wanted to try out different metrics. Now, we explore how
diversely are the communities in which author publishes papers.
The entropy can be calculated as:
H=−
Pn
i=1
p(xi ) log p(xi )
where xi = fraction of papers the author publishes in community i and n = number of communities the author publishes papers in. Community here refers to the community
is paper citation network. The graph below shows the plot
for the entropy of paper publications in different communities versus rank. Thus, we see that highly ranked authors
publish papers in very diverse communities and may be that
is why they became highly ranked. Or it may be that, since
the highly ranked authors have large number of papers, they
are likely to have more collaborators and that too in different
communities in paper citation network. Note that communities in paper citation network represent a research area as
indicated in the community structure section.
Figure 5: Uniformity of citation of papers with decreasing author ranks
The trend in the previous plot will become more clear if we
also plot the number of papers the author writes versus the
rank of the author. An author having large number of papers
6.
COLLABORATION PRACTICES
In this section, we explore the collaboration practices to find
any significant pattern for the top researchers. We begin by
investigating the trend in the number of collaborators and
then go on to explore any possible biases in the kind of
collaborators.
tion. While the observation seems obvious on count, it must
also be noted that several behavioral theories argue for the
presence of complications (due to personality conflicts or
personal idiosyncracies) when two highly noted individuals
collaborate. Therefore, it is not obvious what the answer
should be. In order to answer this question, we perform two
different experiements. In the first experiment, we plot the
average pageRank of the collaborators of a particular author
in decreasing order of his/her rank. The plot is shown in
Figure 9. The curve decreases almost linearly with decreasing influence denoting that the high influence nodes tend
to prefer other high influence nodes for collaboration. It is
important to note here that the pageRank was calculated in
the citation network and not the collaboration network, so
it was not obvious that the collaborators of a high pageRank individual will also have a high pageRank, although this
does turn out to be the case.
Figure 7: Author entropy with decreasing author
ranks
Figure 8 shows the log-plot for the number of unique collaborators for the researchers in decreasing order of their
ranks. As is seen from the plot, the number of collaborators decreases as the rank of the author decreases. However,
the decline is not very prominent, which is understandable
because the number of collaborators will be proportional to
the number of papers and, as noted in Section 3, the pageRank in author citation network does not have a very good
correlation with the number of papers.
Figure 9: Average pageRank score of collaborators
with decreasing rank
Figure 8: Number of collaborators with decreasing
rank
Having observed the number of collaborators, we now try to
investigate the kind of collaborators preferred by the more
influential researchers, i.e. whether highly influential researchers tend to prefer similar researchers for collabora-
In order to confirm our observation, we perform another experiment. We construct a sub-graph of the collaboration
graph by considering only the nodes with ranks within a
certain fixed range of a given node’s rank so that only those
nodes which have pageRank very close to the given node’s,
remain in the network. We then find the clustering coefficient of the resulting sub-graph. The clustering coefficient
in the sub-graph will give us a measure of how likely the
nodes are to collaborate amongst themselves. We then plot
the clustering coefficient for all nodes in decreasing order
of their rank. The plot is shown in Figure 10. It can be
seen from the plot that the clustering coefficient decreases
steadily with decreasing influence. The more influential authors have a high clustering coefficient, once again signifying
that they tend to prefer each other when it comes to collaborating for research. Note that even though the original
graph had a lot of cliques and hence, a high clustering coefficient, the subgraph will break all those cliques and the
clustering coefficient in the subgraph is therefore not biased
because of it. In case it still retains those cliques, that just
reinforces the strong collaboration relationship among those
authors. Besides, we are interested in the declining trend of
clustering coefficient rather than the absolute value.
Figure 10: Clustering coefficient in collaboration
network with decreasing rank
Note that there are a couple of caveats in the reasoning presented above. Firstly, while the above experiments do exhibit high collaboration between the influential researchers,
the given data is insufficient to establish causality, i.e. we
cannot definitively say, with just the given data, whether
they collaborate because they are influential or whether they
became influential because they collaborated. Secondly, the
above said correlation can also be due to the fact that people tend to limit their collaboration to their own institute
(i.e. some geographical factors are at play) and the institute
has some very stringent entry barriers, resulting in the good
researchers collaborating more amongst themselves.
6.1 Uniformity in paper citations of the collaborators
Here we analyze the paper citation uniformity (as in previous
section) of the collaborators of an author. The motivation
behind studying this is to see whether the collaborators a
highly ranked author (who generally has large number of
papers) also have similar uniformity as that of the author.
For this, we plot the mean and standard deviation (Figure
11) of the uniformity in paper citation of the collaborators
of an author versus the page rank of the author.
From the plots, we see that the mean uniformity of the collaborators of an author shows an increasing trend with rank,
while the standard deviation of uniformity of the collaborators shows a decreasing trend with rank. Compare these
plots with the Figure 5. If we look at the values where the
curves start, the standard deviation(0.25) and the uniformity(0.25) in Figure 5 and 0.43 0.25 + 0.25 in mean uniformity curve, it seems that the set of collaborators of highly
ranked author constitutes of some other highly ranked authors but most of the collaborators having very high uniformity(these authors have low ranks Figure 5). These low
rank collaborators are most likely the PhD students.
7.
TEMPORAL CAREER PATTERNS
In this section, we investigate the career graph of a researcher as it evolves over time. The motivation behind this
is to see if there is a specific pattern in the quality and/or
quantity of research of a star researcher with respect to time.
In order to perform this analysis, we first plotted the number of papers and total number of citations for all papers
published in a particular year for some top researchers. The
sample plots for Jeffrey Ullman and Jim Gray are shown
in Figure 12. Similar plots were obtained for other top researchers as well (which we omit here for the sake of brevity).
Some very interesting and useful observations can be made
from these graphs. As is clear from the plots, there seems to
be no definite pattern in the temporal graph of the number of
papers published in an year. However, there is a very interesting pattern in the number of citations in an year (which
is basically the sum of citations received by all papers published in that year). The plots tend to have a prominently
”peaky” nature, i.e., each of the curves is characterised by
the presence of very prominent peaks. This corresponds to
a real world scenario where the researcher tends to focus on
a harder, more time consuming problem which reaps more
dividends as against easier ones which may lead to a flatter
curve. Another very interesting observation is that there
is no corresponding pattern in the number of papers curve
denoting that even though the researcher may be focussing
on a harder problem, he/she does not stop publishing other
papers (a very promising strategy tip for any newbie!).
The given plots can also be interpreted to reconfirm the
notion that the citation practices of researchers are influenced by the quality of papers and not by the influence of
the researcher. This is because, if the citation network had
been influenced by the influence of the researcher, we would
have expected a continuously decreasing power law graph
here (owing to the preferential attachment of every upcoming researcher to the influential node’s papers). This contradicts with the ”peaky” nature observed which can only
be explained by the argument that people tend to vote for
content over influence.
Although the observed pattern is indeed very useful in drawing some important conclusions, it is difficult to comment
just based on the plots for a few researchers. We need to
develop a metric and observe the general trend to be have
statistically significance in our analysis. We observe that the
higher the peak strength(in the temporal citation plot) and
the more early is the peak in the author’s career, the higher
is the rank of the author. This trend we found out by plotting some sample authors. This is intutuive in the sense that
good researches usually take off quite early in their career.
So, we need to design a metric that captures the strength of
the peak and when that peak(in the temporal citation pattern) occured in the author’s career. Thus, we developed a
metric for an author in the following manner and plotted it
pattern for all the researchers:
1. We first need to smoothen out the citation pattern of
an author to remove small random peaks that are not
significant form the view point of an author’s influence(noise). For smoothing, we take a running average (we take the running average for 4 years in our
(a) Mean uniformity of collaborators
(b) Standard deviation of uniformity of collaborators
Figure 11: Mean and Standard deviation in uniformity values
measurements). Let the original curve be denoted by
the function f (t).PThen, the smoothened curve, g(t) is
given by, g(t) = 3i=0 f (t − i)
2. Now, we capture the peaks by taking the difference
function of the smoothened curve (note that we are
dealing with a discrete curve here). We took difference function to capture the peaks(filter out low frequencies). So, the difference function, h(t) correponding to the function obtained in Step 1 will be, h(t) =
|g(t) − g(t − 1)|
3. Multiply every point for the autor with the number of
years since the first publication to obtain the value of
the metric,
P M axi.e., the value of the metric m is given by,
h(t)(t − startT )
m = tt=startT
where startT is the year of first publication and
tM ax denotes the last year plotted(2010)
Not only, does this metric capture the ”peaky” nature of the
curves, it also accounts for the fact that different researchers
may belong to different eras by taking their first publication
year into account. Also, it captures how early an author
takes off in his career by publishing good papers. In Figure
13, the authors are mapped to the X-axis in decreasing order of their influence and the Y-axis shows the value of the
metric for the authors (we follow the binning technique used
in the previous section here as well). As can be seen from
the plot, the value of the metric steadily declines as the influence of the author declines, thus, confirm our observation
on the pattern in the behavior.
In table 4, we list the correlation of our metric with other
influence indices. As is seen from the table and is clear from
the graph, our metric has a high correlation with the citation
pageRank and can be used for measuring a node’s influence
in the network as an alternative to H-index. Also note that,
just like H-index, our metric also depends ’only’ on the local
Figure 13:
ranks
Metric score with decreasing author
attributes of the author and is therefore, fast and easy to
compute locally.
8.
CONCLUSION AND FUTURE WORK
Through the analysis presented in this paper, we can conclude that a successful researcher tends to be a prolific collaborator who collaborates and publishes papers in several
different research topics. Peer group also plays an important role in a researcher’s productivity and good researchers
tend to collaborate and cite each other more. Moreover, a
successful researcher focusses on challenging problems which
require time and garner a lot of citations, however, at the
same time, he/she does not compromise on the quantity of
research as well. Our metric captures this trend very neatly
(a) Temporal citation pattern for Jeffrey Ullman
(b) Temporal paper pattern for Jeffrey Ullman
(c) Temporal citation pattern for Jim Gray
(d) Temporal paper pattern for Jim Gray
Figure 12: Temporal patterns for two top researchers
Table 4: Pearson correlation of different influence
metrics with our proposed metric
Index
Person Correlation
H-index
0.51
pRankAuCollab
0.27
pRankAuCit
0.79
numPapers
0.32
numCitations
0.75
avgCitations
0.22
of citations per paper . It will be interesting to see how
such a metric performs and whether the learned values generalize beyond one network and if yes, then to which kind
of networks. For this purpose we can use some machine
learning technique like ranked SVM to learn some ranking
function which takes into account only local factors and is
able to predict the global ranking of the author. It would be
interesting to study some more temporal citation and collaboration patterns of an author to determine some sort of
causality - does more citation lead to more collaboration or
the other way around.
and can be a good alternative to the H-index.
9.
For future work, we feel that a better metric for an author’s
ranking (than H-indeX) can be learned on the basis of the
various metrics considered in the paper, namely, the number
of papers, the number of citations and the average number
10.
ACKNOWLEDGMENTS
We are extremely grateful to the TAs of the course, especially Cherian Mathew and Chenguang Zhu, for their guidance and support.
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